Respuesta :
Answer:
[tex]3.372-1.96\frac{0.66}{\sqrt{5}}=2.793[/tex]
[tex]3.372+1.96\frac{0.66}{\sqrt{5}}=3.951[/tex]
We are 95% confident that the true mean for the adhesion to solid surfaces in dyne-cm2 is between (2.793; 3.951)
Step-by-step explanation:
Data provided
2.69, 5.76, 2.67, 1.62, and 4.12
We can calculate the sample mean with this formula:
[tex]\bar X =\frac{\sum_{i=1}^n X_i}{n}[/tex]
And replacing we got:
[tex]\bar X=3.372[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma=0.66[/tex] represent the population standard deviation
n=5 represent the sample size
Confidence interval :
The two sided confidence interval for the true mean is given by:
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
We have the confidence level given of 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that [tex]z_{\alpha/2}=1.96[/tex]
Replacing into the formula for the interval we have this:
[tex]3.372-1.96\frac{0.66}{\sqrt{5}}=2.793[/tex]
[tex]3.372+1.96\frac{0.66}{\sqrt{5}}=3.951[/tex]
We are 95% confident that the true mean for the adhesion to solid surfaces in dyne-cm2 is between (2.793; 3.951)
